THE TENSION FIELD OF THE ENERGY FUNCTIONAL ON RIEMANNIAN SUBMERSION

Abstract

In this paper, we will study the tension field of the function related to a Riemannain submersion π : N → M with totally geodesic fibres. In case that the Riemannain submersion π : N → M particularly has a smooth map f : M → N which happens to be a section, we will show that tension field τ (f ) of the energy functional can be decomposed into the horizontal and vertical parts.

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